1.8p. Build a truth table for ~ (p V q) (~q^~p). Is it a tautology? 2....

 

 

Transcribed Image Text:

1.8p. Build a truth table for ~ (p V q) (~q^~p). Is it a tautology? 2. 10p. Suppose that the variables X,Y denote people. Consider the propositional function for X and Y: p(X, Y) means "X likes Y". So p(Ann, Bob) means Ann likes Bob. Write formally the following statement and write its negation in natural language and formally. "If Ann likes someone, then she likes Bob". 3. 7p. Let A, B, C be subsets of U plotted on the Venn diagrams. Describe the shaded area using set operators (union, intersection, difference and complement) 4. 8p. Determine the truth value, justify your answer, 3x EQ VEN: x =y + 2. 5. 6p. Sketch a graph of a function f: [-3,-2] U [2,3] [-4,4] which is one-to-one (is injective), but is not onto [-4,4] (not surjective). 6. 6p. Given relation r, determine the arrow diagram of r, the table form of r, the domain and range of r: 5 T= = {(x,b), (y, b), (y, d), (z, c), (x, d), (y, d), } 7. 6p. Find and show on the real line the domain of the following function: f(x) = 1 x(x+3) + x(x+2) 1.8p. Build a truth table for ~ (p V q) (~q^~p). Is it a tautology? 2. 10p. Suppose that the variables X,Y denote people. Consider the propositional function for X and Y: p(X, Y) means "X likes Y". So p(Ann, Bob) means Ann likes Bob. Write formally the following statement and write its negation in natural language and formally. "If Ann likes someone, then she likes Bob". 3. 7p. Let A, B, C be subsets of U plotted on the Venn diagrams. Describe the shaded area using set operators (union, intersection, difference and complement) 4. 8p. Determine the truth value, justify your answer, 3x EQ VEN: x =y + 2. 5. 6p. Sketch a graph of a function f: [-3,-2] U [2,3] [-4,4] which is one-to-one (is injective), but is not onto [-4,4] (not surjective). 6. 6p. Given relation r, determine the arrow diagram of r, the table form of r, the domain and range of r: 5 T= = {(x,b), (y, b), (y, d), (z, c), (x, d), (y, d), } 7. 6p. Find and show on the real line the domain of the following function: f(x) = 1 x(x+3) + x(x+2)